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LEIPZIG, Germany — I NEVER met my paternal grandfather. He died of the Spanish flu in 1919 at the age of 30, before his children and grandchildren ever got to know him. He was a brilliant mathematician and, as a scientist myself, I feel curious about what he was like. I take consolation from the fact that he lives on in me; after all, a quarter of my genes come from him.

He has been on my mind these past few years, as my research group and I have worked to sequence the genome of a Neanderthal, the closest evolutionary relative of all present-day humans. We have also sequenced a genome from a small bone excavated in a Russian cave close to the border with China; this genome came from a previously unknown Asian relative of the Neanderthals — a group that we call the Denisovans.

These ancient genomes show that the Neanderthals were genetically very similar to us. In fact, for most of the genome, some people living today are closer to the Neanderthals than to other people. Comparing...